It has been known for some time that fluid-saturated rocks have dispersive electromagnetic properties, i.e. frequency-dependent dielectric permittivity and conductivity. Most electromagnetic measurements are designed to determine the electric conductivity of such rocks. Ampère-Maxwell's law states that the electric conductivity σ and the relative dielectric permittivity ∈r are intimately tied as real and imaginary parts of a complex-valued conductivity σ*=σ−iω∈0∈r with the circular frequency ω. Frequently they are also represented as complex-valued permittivity ∈*r=∈r+i(σ/{tilde over (ω)}∈0) with the conductivity scale defined as σ0≡ω∈0.
The electric conductivity and relative dielectric permittivity have different dispersive behaviour: the electric conductivity tends to increase slightly with frequency while the dielectric permittivity decreases strongly, this behaviour is schematically shown in FIG. 1. Extensive laboratory studies have shown that above about 600 MHz the square root of the complex dielectric permittivity of a rock is the volumetric average of the square root of the individual complex dielectric permittivities of the constituting material components. This empirical averaging rule is known as the “Complex Refractive Index Method” (CRIM).
The dispersion behaviour of the electromagnetic parameters of heterogeneous media has been studied throughout the twentieth century. Early work by Peter Debye in the 1920s was subsequently refined by Cole and Cole in the 1950s and others in the 1980s.
The later work clearly showed the dispersion of the dielectric permittivity. At the same time, some dielectric formation-evaluation tools were developed for the oilfield wireline logging industry, notably the EPT (Electromagnetic Propagation Tool) of Schlumberger, operating at 1.1 GHz where the dispersion is minimum. More recently, tools that would measure the dielectric permittivity at several frequencies from 100 MHz to 1 GHz have been developed. Such tools include array dielectric logging tools.
The Deep Propagation Tool, operating at 25 MHz was introduced in the 1970s to provide a dielectric measurement beyond the depth of investigation of the EPT. DPT dielectric measurements were found to be substantially different than those from the EPT, and the tool was not widely used because it was difficult to perform a consistent dielectric interpretation.
A number of techniques have been proposed which use dielectric measurements at different frequencies in the range 106-1010 Hz. Examples can be found in U.S. Pat. No. 5,059,907, U.S. Pat. No. 5,469,062, U.S. Pat. No. 7,376,514, GB2430264 and GB2430265.
This invention is based on the recognition that useful information about formation properties can be obtained from a range of dielectric measurements below 106 Hz.